The present study identified the large-scale tilted ridge and trough (LSTR and LSTT, respectively) axes of the midtropospheric circulation over mid- and high-latitude regions using an objective identification technique that has not previously been applied. In this method, the identification procedure classified contours of 500-hPa height (Z500) fields into three types: the circumpolar wavy contour, the circumpolar contour containing the meridionally overturned (or wave breaking) part, and the locally closed contour. The ridge and trough points were defined on these three types of contours and, subsequently, the ridge or trough axes were identified after connecting successively the nearest ridge or trough points of the neighboring contours under a minimum distance constraint. The performance of the identification method was tested in the daily Z500 fields during 15 November 2011–15 March 2012. The hit rate, false-alarm ratio, and threat score of the method in test reveal that it performs well with a reasonably good skill. An examination of the wave-breaking features during the same period also suggests that the method performs well in the identification of LSTRs and LSTTs for the meridionally overturned parts of the Z500 contours. This objective technique was also applied to an extensive and persistent cold event over East Asia. Results show that the horizontal extent of the Siberian high corresponds well with the zonal extents of the identified LSTR and LSTT. The identification method in the present study might be useful for identifying the key circulation systems associated with extensive and persistent cold air outbreaks during winter.
The large-scale tilted ridge and trough (LSTR and LSTT, respectively) in the midtroposphere, with zonal extents larger than the wintertime climatological ones, sometimes form over mid- and high-latitude regions of the Eurasian continent. They are directly associated with large-scale cold air activities and often cause extensive and persistent low temperature events in Eurasian countries (Bueh et al. 2011a; Peng and Bueh 2012). For example, an extensive and persistent low temperature event occurred in southern China during mid- to late January of 2008, and its key circulation systems were realized as the LSTR, stretching from the Ural Mountains to northeastern Asia, and the accompanying LSTT that extended from middle Asia to East Asia (Tao and Wei 2008; Wen et al. 2009; Zhou et al. 2009; Bueh et al. 2011b, among others). Because of the enormous amount of damage to life and property it caused in China, this cold event aroused extensive public attention and scientific interest.
The long-lasting nature of the LSTR (or LSTT) and the persistent cold event concur with synoptic reasoning, since the time scale of a circulation system is positively proportional to its spatial scale. Further evidence for this observation came from Peng and Bueh (2011), who documented 52 extensive and persistent low temperature events in China during 1951–2008 using observed daily temperatures from 756 meteorological stations in China, and examined their key circulation systems. It was found that a southwest–northeast-tilted large-scale midtropospheric ridge was the key circulation feature common among the wintertime extensive and persistent low temperature events. With the large extent of southward cold advection in association with the LSTR, the Siberian high expanded and amplified with tightened sea level pressure gradients.
The dynamic features of the persistent large-scale ridge and trough system on submonthly time scales have been revealed in several studies. For the persistence of the tilted ridge and trough over the Northern Hemisphere, Zeng (1983) proposed that the ridge and trough tend to intensify barotropically at the expense of the westerly jet, if they are tilted in the northeast–southwest (northwest–southeast) orientation on the northern (southern) side of the westerly jet. On the other hand, Santos et al. (2009) revealed that the strong and persistent midlatitude large-scale ridge system over the northeast Atlantic plays a key role on the extremely dry episodes in western Iberia (Santos et al. 2007). Their results showed that the tropospheric Rossby waves originating from positive height anomalies over North America propagated eastward over the North Atlantic and contributed to the generation and maintenance of the strong and persistent ridge over the northeast Atlantic. Interestingly, they also found that anomalously strong and vertically extended stratospheric positive height anomalies over North America/North Pacific, which were in phase with their tropospheric anomalies, were favorable to the maintenance of the strong ridges over the northeast Atlantic by feeding anomalies at the Rossby wave origin. Wu et al. (2013) found a significant increasing trend of an anomalously strong ridge over northern Eurasia during winter since the late 1980s, and revealed that such a trend corresponded well with that of Arctic sea ice reduction. However, so far the involved dynamics for the wintertime LSTR and LSTT have not yet been systematically investigated in depth. This may be partly due to the lack of an appropriate objective identification method.
Historically, the depiction and thus the detection of the LSTRs and LSTTs have been quite challenging, and no objective identification method has been developed. Generally, over the mid- and high-latitude regions, the upright ridge (or trough) axis in a wavelike flow can be defined by a change in sign of the meridional wind change [i.e., υ = 0 m s−1; Reed et al. (1977)], or as the traverse ridge (or trough) axis by a change in sign of the zonal wind change [i.e., u = 0 m s−1; Li and Zhu (2010)]. However, these diagnostics do not work at the tilted ridge (or trough) axis. In this situation, the position of the tilted ridge (or trough) can be simply defined if the geostrophic vorticity advection disappears (i.e., , where and denote geostrophic horizontal wind and the horizontal gradient of the geostrophic vorticity, respectively), since negative vorticity advection lies ahead of the ridge axis and positive vorticity advection lies behind. However, this method does not work at the ridge or trough axis where the shear vorticity is stronger than the curvature vorticity (Berry et al. 2007). Then, if only the curvature vorticity is taken into account, this diagnostic is capable of identifying the ridge and trough axes, such as those of the African easterly waves (Berry et al. 2007). For brevity, hereafter we call this method the curvature vorticity advection (CVA) method. In the instantaneous synoptic fields, the CVA method works extremely well for identifying the trough and ridge axes (Berry et al. 2007; T. Hewson 2015, personal communication). On the daily mean (or low frequency) field, the CVA method still works well where the troughs and ridges are not heavily tilted. However, large-scale heavily tilted ridges and troughs over mid- and high-latitude regions, which are the primary concern in the present study, could not be adequately identified by the CVA method, probably because of the different horizontal-scale features of time mean (or low frequency) geopotential height and vorticity fields. This issue will be discussed in section 5.
Therefore, for real-time monitoring and advancement of the relevant research an objective method of identifying the LSTRs and LSTTs over mid- and high-latitude regions is necessary. In this paper, we propose a new objective identification method for the LSTR and LSTT that can be applied to any gridded dataset, and highlight the importance of this identification method through analyzing the correspondence between the zonal extent of LSTR (or LSTT) and that of the large-scale cold air activity. The paper is organized as follows: section 2 describes the objective identification method of the LSTR and LSTT. In section 3, we test the skill of this objective technique by comparing the observed and identified daily LSTRs and LSTTs during the winter of 2011/12 (15 November–15 March). In section 4, we apply the method to identify the LSTRs and LSTTs during a well-known East Asian cold event and examine their association with the large extent of cold spell. The final section consists of a summary and discussion.
It is desirable to have a diagnostic that can represent the actual position as well as the zonal extent of the LSTR and LSTT, which is easy to generate in real time with minimal computation from observed or modeled fields. For this purpose, in this study we chose the LSTR and LSTT axes at 500 hPa as the core diagnostics, as they have an intimate relationship with the extensive cold air activity in the lower troposphere.
In the present study, we adopted another strategy for the identification of large-scale ridges and troughs, which differs from that of the CVA method. Specifically, for identifying ridge or trough axes, we searched the lines (or axes) along which the contours of 500-hPa geopotential height field (Z500) had the local maximum curvatures.
As is empirically known, the LSTR often passes through the blocking high, such as the blocking high over the Ural Mountains, or the locally isolated cutoff high [it cannot be recognized as blocking when its longitudinal extent is not large enough to satisfy the blocking criteria; Tibaldi and Molteni (1990)]. Similarly, the LSTT also often goes across the regional cutoff low. Therefore, it is also necessary to properly identify the LSTR and LSTT axes within the regions of blocking high and cutoff low.
Based on the daily Z500 fields of the NCEP–NCAR reanalysis data (Kalnay et al. 1996), the identification process of the LSTR (or LSTT) axis consisted of four steps. First, the low-pass-filtered Z500 fields were obtained using a Lanczos low-pass filter (Duchon 1979), with the cutoff period of 8 days and 121 weights. (The frequency response of the filter is shown in Fig. A1 of the appendix.) Then, different types of contours on the filtered Z500 field were recognized and their constituting points were recorded accordingly. Subsequently, the ridge points and trough points on different types of contour were identified. Finally, each LSTR (or LSTT) axis was defined based on the identified ridge (or trough) points.
1) Different types of contours
In the Northern Hemisphere, we first found the contour with the minimum geopotential height, , and then drew out every contour with an interval of 5 m until reaching the maximum contour, , at 5840 m. This upper bound was chosen to exclude the regions with characteristically tropical or subtropical heights, as our aim was to identify the LSTR and LSTT over mid- and high-latitude regions.
According to the relative position to the North Pole, the contour was simply recognized as either the circumpolar contour or the locally closed contour. All constituent points of a given circumpolar contour defined by longitudes and latitudes were recorded by every 2.5° longitude according to the order in which they appeared from west to east, in which is the serial number, the longitude [λ(1) = 0° and λ(N) = 357.5°], is the latitude, and is the number of constituent points. If the circumpolar contour was a wavy type (dotted contour in purple in Fig. 1) without a meridionally overturned part, . If the circumpolar contour contained the meridionally overturned part (dotted contour in red in Fig. 1), . For a locally closed contour (dotted contour in blue in Fig. 1), the longitudinal distance between the western- and easternmost points, , should be less than 357.5° with the first constituent point chosen arbitrarily.
2) Ridge and trough points
(i) Circumpolar wavy contour
We now introduce how ridge and trough points for a given circumpolar wavy contour were determined. Since a ridge (or trough) axis was naturally situated between two neighboring node points where the sign of the curvature vorticity changes, we first identified all the node points of the contour. Before identifying the node point, we needed to define a slope for the line segment connecting points Pi and Pi+1 of the contour. The slope, , was defined in terms of the latitude and longitude of Pi and Pi+1, and expressed as
Then, each node point was simply defined by . The point Pi was defined as the node point in front of the trough and behind the ridge, if attained a maximum value (point A in Fig. 2). Similarly, the point Pi was defined as the node point in front of the ridge and behind the trough, if attained a minimum value (point B in Fig. 2). To eliminate spurious node points, every point of the circumpolar wavy contour was smoothed by a nine-point smoothing method with itself as the central point, and then each node point was defined only if its corresponding was greater (or less) than those of its two neighboring points to the west and the other two neighboring points to the east.
A ridge or trough point can be identified between two neighboring node points with opposite signs of , according to the bending angle of the contour. As shown in Fig. 3, the three consecutive points on a contour, Pi−1, Pi, and Pi+1, form a triangle, and the bending angle at Pi can be determined in terms of the law of cosines:
where a, b, and c are the lengths of the triangle’s three sides, determined by the latitudes and longitudes of the triangle’s three vertices.
Since represents the degree of bending of the contour, the ridge or trough point was simply defined as the point with the minimum . Specifically, a ridge point was defined if the point with the minimum was identified between the node point with the maximum to the west and the node point with the minimum to the east, as shown in Fig. 2. Similarly, a trough point was defined if the point with the minimum was identified between the node point with the minimum to the west and the node point with the maximum to the east. Hereafter, this identification method is referred to as the minimum bending angle (MBA) method. In practice, the MBA method is considered to be valid only when is no more than 177°. We tried different values of , from 175° to 178°, and 177° was the best option, as no ridge or trough point was defined for the considerably smooth contour.
(ii) Meridionally overturned part of the circumpolar contour
For the meridionally overturned part of a circumpolar contour (see the dotted contour in red in Fig. 1), the setting of node points was not applicable, in contrast to the situation of the wavy part of the contour. As for the meridionally overturned part, it holds that . Theoretically, for a given contour, if an anticyclonic overturning starts to occur at a point, like point A in Fig. 4a, it holds that , according to Eq. (1), due to and . This situation is analogous to the anticyclonic wave breaking of the transient baroclinic wave (Peters and Waugh 1996; Pelly and Hoskins 2003), with the point A corresponding to a ridge point. If a cyclonic overturning starts to occur at a point, like point A in Fig. 4b, it holds that , due to and . This situation is analogous to the cyclonic wave breaking of the transient baroclinic wave (Peters and Waugh 1996; Pelly and Hoskins 2003), with point A corresponding to a trough point. A ridge–trough pair, as indicated in Figs. 4a and 4b, corresponds to the meridional reversal of the absolute vorticity (Rivière et al. 2010), which may be regarded as blocking if the horizontal scale is sufficiently large (Tibaldi and Molteni 1990). As for the identification of the ridge and trough points in this situation, in practice, it is unnecessary to seek . Instead, once the condition was satisfied for a segment of contour (crossed points in Figs. 4a, b), we determined the ridge and trough points. Following a given contour from west to east, if the contour was anticyclonically overturned (oriented southwestward), as in Fig. 4a, the ridge point was defined as the first ith point that satisfied the conditions and , as indicated by point A in Fig. 4a. The trough point in this situation was defined as the last ith point that satisfied the conditions and , as indicated by point B in Fig. 4a. Analogously, if the contour was cyclonically overturned (oriented northwestward), as in Fig. 4b, the trough point was defined as the first ith point that satisfied the conditions and , as indicated by point A in Fig. 4b. The ridge point in this situation was defined as the last ith point that satisfied the conditions and , as indicated by point B in Fig. 4b. It should also be pointed out that if a contour in the low-frequency Z500 field starts to be overturned meridionally at one longitude, two points of the contour always occur at the same longitude. But in fewer cases, only one recorded point occurs at the meridionally overturned longitude. These two situations were separately given in Figs. 4a and 4b, trying not to lose either of them.
(iii) Locally closed contour
Since the LSTR and LSTT axes often passed through the locally closed contours, we expected to recognize them within the locally closed contour. In this situation, the above identification method was not applicable. With the recognition of all locally closed contours, as introduced in section 2b(1), here we identified the ridge and trough points in terms of the local maximum curvature points on the contour, in which the local maximum curvature was determined by the local minimum bending angle [see Eq. (2)]. However, we noticed that the recording method of the constituent points for the circumpolar contour was inappropriate for a locally closed contour. For example, let us look at a simple case of circle. If the points on the circle were recorded by every 2.5° longitude, as in Fig. 5a, the recorded points would be unevenly distributed, in which the points near the westernmost and easternmost points would be farther apart. As a result, the curving at the westernmost and easternmost points would be overestimated and the identified troughs and ridges would thus bias toward east–west-oriented ones. To reduce this bias, we altered the recording way of the points on the circle, for which every point at which the circle intersects the grid lines was recorded, as in Fig. 5b. As seen in Fig. 5b, this way of recording would increase the number of circle points and reduce the above-mentioned bias. Therefore, here we adopted the recording way in Fig. 5b to the contour points of the locally closed contour. Specifically, for a given closed contour, those points at which the contour intersects the grid lines (2.5° × 2.5°) were recorded, as in Fig. 5c, and then those were used for the identification of local maximum curvature points.
As indicated in Fig. 5c, there were two types of local maximum curvature points on the locally closed contour, namely the convex point (see point A in Fig. 5c) and the concave point (see point B in Fig. 5c), respectively. In practice, a convex (concave) point was defined at Pi (ith point) if the central point (Pc1) of the segment connecting points Pi−1 and Pi+1, and the central point (Pc2) for points Pi−2 and Pi+2, were both situated inside (outside) the contour. Then, for a closed contour with geopotential height increasing outward (i.e., the closed low) a convex (concave) point Pi was recognized as the trough (ridge) point with an additional constraint of the bending angle less than 160°. In the same way, a convex (concave) point on the contour of the closed high was recognized as the ridge (trough) point. With this method, points A and B in Fig. 5c were clearly identified as the trough and ridge points, respectively. In addition, as seen in Fig. 5c, other two convex points C and D could also be identified as the trough point. We tried different upper bounds of , from 130° to 170°, and 160° was the best option. As will be shown in the next section, with this upper bound of , the identification method performs well for a locally closed contour in distinguishing the ridge and trough points from those of the circular portion.
3) Ridge and trough axes
The identification of the ridge (or trough) axis was based on the fact that it consists of a number of nearby ridge points (or trough points) on different contours and can be recognized by some objective criteria. As for the ridge axis, the algorithm started from each ridge point of the contour with (5840 m) and found its nearest ridge point on the nearby contours in the decreasing order of . The recognition of whether or not these two ridge points belong to the same ridge axis was achieved in the following two steps. 1) Condition A: if , these two ridge points were recognized as belonging to the same ridge axis, where d denotes the distance between two neighboring ridge points and represents a threshold distance. If the condition A was not satisfied, the recognition process moved to the next step. 2) Condition B: if and the difference between these two ridge points was less than 50 m, these two ridge points were recognized as belonging to the same ridge axis, where represents a relaxed threshold distance. It was always observed that the distance between two neighboring contours was larger in some regions where contours were distributed sparsely. Therefore, in order to keep the continuity of the same ridge (or trough) axis in this situation, it was necessary to relax the minimum distance requirement. If the condition B was also unsatisfied, the identification process for the ridge axis ended, and the next identification process began for the contours with the lower . Here, and were taken as 500 and 800 km, respectively, with the former being approximately equal to the horizontal spacing of two meshes and the latter being three to four meshes, considering the data resolution of (2.5° × 2.5°). In this manner, all ridge points belonging to the same ridge axis were successively identified, and further all ridge axes were identified by linking their constituent ridge points. All trough axes were identified in an analogous manner, except that identification process began from each trough point of the contour with (minimum geopotential height) and searched for its nearest trough point on the nearby contours in an increasing order of Z500.
In fact, condition A is a statement of the nearest principle for a ridge or trough axis, and implicitly assumes that there is only one ridge (or trough) axis within a horizontal distance of . Empirically, this assumption is consistent with the large-scale midtropospheric circulation features. Condition B is a necessary supplement to condition A, by relaxing the minimum distance requirement between two neighboring ridge (or trough) points, but with the demand of a smaller difference between them. For example, in a case from 13 January 2008, as shown in Fig. 6a, taking only the condition A into account, the complete trough axis from Lake Baikal to the Sea of Okhotsk, which is apparent in the manual visualization, would be interrupted and identified as two short trough axes. Additionally, a pair of ridge and trough axes straddling the Caspian Sea in the manual visualization would disappear or apparently shorten. Adding condition B, the neighboring ridge (or trough) points were reasonably connected within the sparsely distributed contours and the complete ridge (or trough) axes were well represented, as displayed in Fig. 6b.
Since the LSTR and LSTT were our primary concern, we eliminated the small ridge and trough axes with horizontal length less than 1000 km. The length of the ridge or trough axis was defined as the spherical distance between the start and end point of the same ridge or trough axis, and the spherical distance was determined only by the longitudes and latitudes of the start and end points. Furthermore, in order to keep the large-scale smooth feature of the LSTR and LSTT, every ridge or trough axis was smoothed by the 15-point smoothing method, through averaging longitudes and latitudes of the neighboring 15 ridge or trough points for a given ridge or trough point, with itself as the central point. Finally, we eliminated all ridge and trough points identified to the north of 80°N. The method is inadequate to depict the ridge and trough axes crossing the polar region, because its recording way of contour points relies on longitudes (e.g., every 2.5° longitude for the circumpolar contour).
3. Skill of the objective technique
In this section, we use the daily Z500 fields during the winter of 2011/12 (15 November–15 March) to test how well the objective identification method works, through comparing the identified LSTR and LSTT axes and their observed counterparts. Since the observed LSTR and LSTT axes are not available, their equivalents were subjectively plotted in the daily Z500 fields with a careful visual inspection, which may be considered to be those generated by an experienced analyst. Hereafter, such an equivalent is called the “observed” LSTR (or LSTT) axis. The test includes two parts. First, we evaluate the reliability of the identification method in terms of its hit rate (HR), false-alarm ratio (FAR), and threat score (TS); then, to the meridionally overturned part of a circumpolar contour, we examine if the identification is consistent with the Rossby wave–breaking feature in the mid- and upper troposphere.
a. Hit rate, false-alarm ratio, and threat score
To evaluate the reliability of the objective technique, following the notion of the skill in a probability forecast, we calculated the HR, FAR, and TS of the identification method, based on the numbers of the “observed” and identified LSTRs and LSTTs in the daily fields during the period from 15 November 2011 to 15 March 2012 (122 days). The data used here (and also in section 4) were the daily meteorological fields of the NCEP–NCAR reanalysis (Kalnay et al. 1996).
The HR, FAR, and TS are defined, in an analogous way of Mason (1982), as
where O and I denote the total numbers of the observed and identified LSTRs (or LSTTs), respectively, and H the number of “hits,” for which an LSTR (or LSTT) was both observed and identified. Accordingly, the I − H represents the number of false alarms and the FAR is defined relative to the number of the identified LSTRs (or LSTTs). As inferred from the definitions, for perfect identifications, the HR, FAR, and TS should be 1, 0, and 1, respectively.
Figure 7 shows the identified LSTRs and LSTTs (left column) and those in the subjective plotting (right column). The daily plots are displayed once a week. Table 1 shows the HR, FAR, and TS of the identification method. If one visually checks the identified LSTRs and LSTTs (left column) and compares them to their counterparts in the subjective plotting (right column), the identification method performs reasonably well throughout the winter of 2011/12. It is also true if we check the identified LSTRs and LSTTs in all daily plots (not shown). In fact, as listed in Table 1, its HR for the LSTRs (LSTTs) is high, approximately 0.97 (0.96), consistent with its high TS of 0.92 (0.93). Even for the ridge (trough) axes with a zonal extent larger than 60° longitude, the method also shows a high HR of 0.94 (0.92).
However, as seen in Table 1, as compared to those with a horizontal length larger than 1000 km, the ridge and trough axes with a zonal extent larger than 30° longitude were identified with a lower HR, and hence a lower TS. With careful checking, it is found that if an observed larger-scale ridge (or) trough axis goes across the very flat contours (the minimum exceeds the upper bound of 177°), sometimes it is disrupted into two shorter segments in identification. For example, on 15 November 2011, a northwest–southeast-oriented LSTT was observed over the North Pacific between 150°E and 150°W, but it was identified as two short troughs. According to the HRs listed in Table 1, this sort of disruption occurs up to 9% for the ridge and trough axes with a zonal extent larger than 30° longitude, whereas it occurs only up to 4% if all of the ridges and troughs with a horizontal length larger than 1000 km are taken into account.
The FAR for the method is relatively low, up to 5% (4%) for the LSTRs (LSTTs). In particular, for the ridge and trough axes with a zonal extent larger than 45° longitude, it performs without a false alarm. In addition, after examining the daily maps throughout the winter of 2011/12, we found that the identification method works remarkably well for the ridge and trough axes within locally closed contours, without a missing or false alarm. The HR, FAR, and TS for the test reveal that, on the whole, the method presented in section 2 has a reasonably good skill in the identification of LSTRs and LSTTs.
b. Meridionally overturned part of the contour and Rossby wave breaking
The meridionally overturned part of the Z500 contour, which occurred frequently during the period from 15 November 2011 to 15 March 2012 (Fig. 7), in fact, corresponds to a local reversal of potential vorticity (PV) gradient and thus reflects the presence of the Rossby wave breaking (Rivière 2009; Rivière et al. 2010). In this subsection, by examining the wave-breaking feature, we assess the robustness of the methodology in the identification of the LSTRs and LSTTs around the meridionally overturned parts of the contours.
In most of the current detection methods, the Rossby wave–breaking event was identified at the tropopause and the main emphasis was placed on the synoptic wave-breaking (e.g., Postel and Hitchman 1999; Martius et al. 2007; Strong and Magnusdottir 2008; Rivière et al. 2010; Ndarana and Waugh 2011). Therefore, it is not appropriate to apply them directly to evaluate the methodology in the present study, in which we used the low-pass-filtered Z500 fields. For our purpose here, we have developed a simple detection method of Rossby wave breaking, following the method of Rivière et al. (2010).
The detection method of Rossby wave breaking here consists of four steps. First, the PV fields were first calculated on the isobaric surfaces using the low-pass-filtered daily wind and temperature fields and then the resultant isobaric PV fields were linearly interpolated to the isentropic surfaces, as in Ndarana and Waugh (2011). The low-pass-filtered wind and temperature fields were obtained with the Lanczos low-pass filter in the appendix, which match well with the low-pass-filtered Z500 fields in our method in the identification of LSTRs and LSTTs. For the details of the PV calculation and interpolation, readers are referred to Ndarana and Waugh (2011). Second, on each of the isentropic surfaces of 320, 330, 340, and 350 K, the PV contours at 0.5-PVU (1 PVU = 10−6 K kg−1 m2 s−1) intervals over all values of PV present were generated. Then, the PV contours that are circumpolar were retained and those with isolated pockets of high- or low-PV air, which are not associated with wave breaking, were excluded, using the same technique as in Strong and Magnusdottir (2008) and Rivière (2009). At each day, on each isentropic surface, the points of the PV contour at which there is a meridional reversal of the PV gradient were identified to be related to be Rossby wave breaking, following the method of Rivière et al. (2010). As indicated by the schematic in Figs. 8a and 8b, the thick dashed parts (from Pi to Pf) stand for the wave-breaking portions of the PV contours. For more details in the identification of wave breaking, readers are referred to Rivière et al. (2010). Third, we divided wave breaking into the anticyclonic wave breaking (AWB) and cyclonic wave breaking (CWB) on each of the four isentropic surfaces. As shown in Fig. 8, if the first point Pi along the wave-breaking part of the contour is more to the south (north) than the point Pb, which is the previous point (searched backward in the reverse orientation of the arrows) along the PV contour at which the meridian (thin dashed line) passing through Pi intersects the PV contour, all of the points from Pi to Pf (the last point of the wave-breaking part) are considered to be related to an AWB (CWB). The region of AWB (CWB) is crosshatched in Fig. 8a (Fig. 8b) in pink (green). On each isentropic surface, the wave-breaking feature (anticyclonic or cyclonic) at each grid point was simply represented by a wave-breaking index (WBI). The WBI is set as 1 (−1) at the grid point that is related to an AWB (CWB) and as 0 at the grid point without wave breaking. Finally, at each grid point, we averaged the WBIs on the four isentropic surfaces with the same weight and determined the wave-breaking feature at that grid point. Specifically, the grid point is recognized as related to an AWB (CWB) if the averaged WBI at that grid point is not lower (higher) than 0.25 (−0.25). At a given grid point, the threshold value of the averaged WBI means that, even though the wave breaking occurs only on one of the four isentropic surfaces, it is also recognized as wave breaking. In addition, the importance of vertical averaging of the WBIs over several isentropic surfaces was discussed in detail in Michel and Rivière (2011).
The regions of Rossby wave breaking in the daily fields during the winter of 2011/12 were indicated by crosshatches in the left column of Fig. 7. Generally speaking, the region of wave breaking is always embedded between the LSTR and LSTT, as indicated in Fig. 8. From mid- to late November (top three rows), Z500 contours were meridionally overturned over the regions from eastern Europe to middle Asia, corresponding to the occurrences of AWB (pink crosshatches). In this period, the LSTRs and LSTTs were identified between 20° and 80°E, matching well with the region of AWB. For example, on 22 November, a pair of southwest–northeast-oriented LSTR and LSTT were identified over the above-mentioned region within the meridionally overturned parts of contours and their locations and extents are consistent with the region of AWB. On 15 November, CWBs (green crosshatches) occurred over the northwest and northeast Atlantic, in good correspondence with the identified troughs and ridges. From 6 December 2011 to 10 January 2012, the Northern Hemisphere circulation mainly shows a wavelike structure and thus the observed meridionally overturned parts of Z500 contours have a smaller zonal extent. During this period, the identified ridges and troughs for the meridionally overturned parts of contours are consistent as well with the local wave-breaking features (AWB or CWB).
During 17–24 January [top two rows of Fig. 7 (continued)], an impressive CWB event occurred over northwestern Pacific, in conjunction with the southeastward intrusion of the cutoff low of polar origins. The identified trough and ridge axes over this region consistently clamped the region of CWB. The ridge and trough axes identified over Europe also correspond well with the regional AWB.
From late January to mid-February, most strikingly, the circulation over the mid- and high-latitude Eurasia primarily showed the wave-breaking feature in a large zonal extent. During this period, the Eurasian countries experienced a strong and persistent cold wave (WMO 2012; Vries et al. 2013). On 31 January, to the east of 60°E, the two transverse ridges identified over northern Asia and the troughs to the south are consistent well with the region of AWB. Over the northern part of Europe, there was a lack of ridge identification, whereas an AWB occurred over the region. As discussed in section 3a, this is primarily due to the sparse Z500 contours, within which the methodology fails to identify the ridge or trough axis. From 7 to 14 February, AWBs occurred locally over several parts of the Eurasian continent, matching as well with the identified LSTRs and LSTTs. Besides, the CWBs detected over the northeastern Pacific during this period also correspond well with the identified ridges and troughs.
From late February to mid-March, the Northern Hemisphere circulation was recovered from the striking wave-breaking state in the earlier period. Thus, the observed meridionally overturned parts of Z500 contours showed a smaller zonal extent. During this period, the identified ridges and troughs for the meridionally overturned parts of contours were also in good correspondence with the local wave-breaking features.
It should be pointed out that the detection of wave breaking is based on the PV fields and the latter have a finer scale than the Z500 fields (Hoskins et al. 1985), though the low-pass-filtered wind and temperature fields were used in the PV calculation. It means that, on a finer scale, the identified LSTRs and LSTTs in the present study are not necessarily in good agreement with the detailed features of wave breaking.
With a careful examination, the wave-breaking features in daily fields throughout the winter of 2011/12 reveal that the methodology performs remarkably well in identifying LSTRs and LSTTs for the meridionally overturned parts of the Z500 contours.
4. Application of the methodology to an East Asian cold event
In this section, we apply the objective identification method of large-scale tilted ridge and trough axes, as described in section 2, to a well-known East Asian cold event, to examine how the identified LSTR and LSTT are associated with persistent large-scale cold air activity. The case chosen here is the East Asian cold event that occurred during the period from 26 December 1954 to 17 January 1955. It was a long-lived cold spell that happened under the background of the protracted La Niña event of 1954–56 (Lau et al. 2006; Peng and Bueh 2011; Bueh et al. 2011a). In addition, this cold event was characterized by persistent and frequent LSTRs and LSTTs with a large zonal extent (Bueh et al. 2011a). The main purpose in this section is to highlight the importance of the identification method for the detection of the key circulation system typical of the extensive and persistent cold temperature event.
Figure 9 shows the evolution at 3-day intervals of the Z500 fields (contours) and the identified LSTRs (red lines) and LSTTs (blue lines) during 26 December 1954 to 17 January 1955. Throughout the cold event, LSTRs and LSTTs with a zonal extent larger than 30° longitude appeared persistently and frequently over the Eurasian continent and they are successfully identified by our objective identification method.
A natural question that immediately follows is how these LSTRs and LSTTs are associated with the Siberian high (SH) and thus the extensive and persistent cold event over East Asia. Synoptically, influences of the LSTR and LSTT on the SH can be understood from the perspective of the well-known quasigeostrophic height tendency equation [see Eq. (8.4) of Martin (2006)]. According to the equation, amplification of the near-surface anticyclone results from cold temperature advection that increases with height from the surface to midtroposphere. The presence of the midtropospheric LSTR and LSTT couplet over the Eurasian continent would be consistent with a large extent of cold air advection aloft, as the near-surface temperature advection over the Siberian region, as a whole, is rather weak, thus causing an extensive amplification of the SH. On the intraseasonal time scale, Takaya and Nakamura (2005) investigated the amplification process of the SH using the PV inversion technique. They revealed that in the upper troposphere a blocking ridge over western and central Siberia and its accompanying trough to the southeastern side, as components of a quasi-stationary Rossby wave train propagating across the Eurasian continent, act to reinforce the SH [see Figs. 3 and 7 in Takaya and Nakamura (2005)]. Therefore, it suggests that the LSTR and LSTT couplet, as the large-scale example of the upper-tropospheric pattern associated with the strengthening of the SH, could possibly cause the extensive amplification of SH. This hypothesis was further supported by the observational evidences in Bueh et al. [(2011a), see their Figs. 1 and 3].
We now examine the LSTRs and LSTTs in the daily fields and their association with the cold temperature anomalies over East Asia during the cold case of 1954/55. The surface air temperature (SAT) anomaly fields for the case are displayed in Fig. 10, with the 1030-hPa isobar of sea level pressure superimposed (bold black contour). For brevity, day 0 refers to the starting day of the cold event and day N (−N) stands for the day that is N days after (before) day 0. At day −3, a southwest–northeast-oriented LSTR (zonal extent of ~80° longitude) straddled the regions from middle to northeast Asia and a zonally oriented trough was formed to its south (Fig. 9a). The latter was connected with a cold low over the northwestern Pacific, as indicated by the closed contours. At the same time, the SH was amplified and expanded, as indicated by the isobar of 1030 hPa (Fig. 10a), leading to extensive cold air accumulation around central Siberia. With the initiation of the cold event at day 0, the LSTR apparently extended northeastward to the northern side of the Bering Strait, spanning a zonal extent of ~140° (Fig. 9b). The cold SAT anomalies were strengthened over eastern Siberia and the Bering Strait, as the isobar of 1030 hPa still covered the region around the Bering Strait (Fig. 10b). Over northern China, both the isobar of 1030 hPa and the isoline of −4°C slightly moved southward. The above analysis suggests that the SH amplification is closely associated with the accompanying LSTR and LSTT. From days 3–6, the LSTR was slightly shortened, but still maintained its zonal extent of ~90° longitude (Figs. 9c,d). Correspondingly, the northeastern portion of the SH shrank westward (Figs. 10c,d). From days 9–12, the zonal extent of the tilted ridge was further shortened (Figs. 9e,f), matching well with the shrinking of the horizontal extents of both the SH and cold SAT anomalies over East Asia (Figs. 10e,f). During this stage, the tilted ridge slightly moved southward and the corresponding isobar of 1030 hPa and the contour of −4°C also approached the southeastern coast of China. So, it is shown that the horizontal extent of SH has a close association with the zonal extents of the accompanying LSTR and LSTT. Up to day 12, the LSTR and LSTT showed an AWB feature. During days 15–18 (Figs. 9g,h), such an AWB feature was considerably weakened and cold SAT anomalies mainly dominated over eastern China (Figs. 10g,h). The broader extent of the ridge corresponded well to the large extent of warm SAT anomalies over northern Asia (Figs. 10g,h). At day 21, the AWB appeared again between the LSTR and LSTT, and the related cold SAT anomalies were strengthened over the region of northeastern China and Yakutsk (Figs. 9i and 10i). With the prevalence of warm SAT anomalies over central Siberia at day 24, the cold surface temperature anomalies associated with the LSTR were basically restricted over southern China (Fig. 10j).
As shown in Figs. 9 and 10, it is clear that the identified LSTR and LSTT, on the whole, have a close association with the extensive amplification of the SH, as suggested by Takaya and Nakamura (2005). The LSTR and LSTT couplet corresponds considerably well with the large extent of the “cold south–warm north” SAT anomaly pattern over the Eurasian continent, which was recognized as the key characteristic of extensive and persistent low temperature events over East Asia (Tao and Wei 2008; Wen et al. 2009; Zhou et al. 2009; Bueh et al. 2011b).
Since blocking is closely associated with the cold air accumulation over central Siberia and its following outburst toward East Asia (Yihui 1990; Takaya and Nakamura 2005), here we examine its daily evolution during this event (Fig. 11). Two kinds of blocking indices were applied in the present study. The first was the well-known Tibaldi and Molteni (1990) index (referred to as the TM90 index), which was based on the fact that blocking occurs where the meridional Z500 gradients are locally reversed around 50°N. The second was developed by Pelly and Hoskins (2003) from the perspective of wave breaking (referred to as the PH03 index) and blocking was defined as where the meridional potential temperature gradient on the potential vorticity surface near tropopause (e.g., 2-PVU surface) is locally reversed. In fact, Rossby wave breaking (or blocking) measured by the PH03 index also reflected the local reversal of the meridional PV gradient, which was presented in section 3b of the present study (see also Fig. 8). For more details of these two blocking indices, readers are referred to Tibaldi and Molteni (1990) and Pelly and Hoskins (2003). From days −3 to 6, the blocking circulations over the Ural Mountains, central and eastern Siberia were well represented by the both TM90 and PH03 indices, consistent with the meridionally overturned contours of the Z500 fields (Figs. 9a–d). The blocking circulation over eastern Siberia from days 17 to 24 was also indicated by the PH03 index, whereas it was absent in the TM90 index configuration. For this cold event that persisted for 23 days, however, the whole story of the cold SAT anomalies could not be explained completely by regional blocking over northern Asia, although the latter corresponded well with the cold anomalies for some time slices of the whole event. For example, during days 9–17, blocking was absent according to the two indices (Figs. 11a,b). Instead, the cold SAT anomalies during this event were accompanied by the LSTR and LSTT (Fig. 9). This suggests that, for the extensive and persistent cold event over East Asia, the LSTR and LSTT axes might be considered as appropriate detection diagnostics.
5. Summary and discussion
We presented an objective identification method for the LSTR and LSTT axes in the midtropospheric circulation over mid- and high-latitude regions that has not previously been applied in either research or operational areas. The algorithm classified the contours into the circumpolar wavy contour, circumpolar contour containing the meridionally overturned part (wave breaking part), and the locally closed contour. Then, the ridge and trough points were defined on the three kinds of contour of the Z500 field and subsequently the ridge or trough axes were identified after connecting successively the nearest ridge or trough points of the neighboring contours under the minimum distance constraint.
The reliability of the objective identification method was evaluated in terms of its hit rate, false-alarm ratio, and threat score, based on the numbers of the “observed” and identified LSTRs and LSTTs in the daily Z500 fields during 15 November 2011 to 15 March 2012. The hit rate, false-alarm ratio, and threat score of the identification method are 0.97 (0.96), 0.05 (0.04), and 0.92 (0.93), respectively, for the ridge (trough) axes with the horizontal length larger than 1000 km. These scores reveal that the identification method performs well with a reasonably good skill. In addition, during the same period, we examined the wave-breaking features in daily fields and found that the method performs remarkably well in identifying LSTRs and LSTTs for the meridionally overturned parts (or wave-breaking parts) of the Z500 contours.
We also applied this objective technique to a well-known East Asian cold event and examined how the identified the LSTRs and LSTTs are associated with the large extent of cold air activity. The observed LSTRs and LSTTs during this event were successfully depicted by the identification method. It is shown that the LSTR and LSTT axes might be appropriate diagnostics for the detection of the key circulation system typical of the extensive and persistent low temperature event over East Asia. Yet, it should be pointed out that as the LSTR and LSTT have been recognized as the key circulation feature common among the extensive and persistent cold events over East Asia (Bueh et al. 2011a; Peng and Bueh 2011), it is still unknown whether they also work in the cases without cold air outbreak. This issue remains for future work.
The CVA method was verified as effective in identifying the ridge and trough axes in the synoptic fields (Berry et al. 2007). To examine its performances in the instantaneous and the low-frequency fields, we show the identified troughs and ridges with the CVA method (see http://www.atmos.albany.edu/student/gareth/source.htm) in Figs. 12a and 12b. Figure 12a just corresponds to the instantaneous Z500 field, but Fig. 12b is created on the basis of the low-pass-filtered (with an 8-day cutoff) Z500 field, which could be directly compared with the corresponding result of the current study (Fig. 12c). As shown in Fig. 12a, the CVA method works almost perfectly in the instantaneous Z500 field (1200 UTC 15 January 1955), with a reasonable identification of the troughs and ridges everywhere. In the low-pass-filtered daily mean field (15 January 1955), as shown in Fig. 12b, the CVA method still works well where the troughs and ridges were not heavily tilted. However, the CVA method is somewhat inadequate to identify the heavily tilted ridges and troughs in the time mean (or low frequency) field, whereas they (LSTRs and LSTTs) are the primary concern in the present study. For example, the observed tilted ridge extending from middle Asia to far eastern Russia in Fig. 12b was not well identified with the CVA method. One may infer from Figs. 12a,b that the smaller-scale depiction of the curvature vorticity advection term in this method is an advantage in the instantaneous Z500 field, but it might be a disadvantage for portraying the LSTR and LSTT in the low-frequency field. It also reflects that the time mean Z500 field and its corresponding vorticity field show different horizontal-scale features. In comparison, the LSTRs and LSTTs were reasonably well illustrated by our identification method, as shown in Fig. 12c. It seems that, to depict ridge and trough axes, the curving of the Z500 contour itself is adequate for the large-scale circulation structure in the low-frequency field.
In section 4, we have discussed the possible connection between the LSTR–LSTT couplet and the SH. Generally speaking, the zonal extents of the LSTR and LSTT axes have a good reference meaning to the horizontal extent of the SH. However, the amplitude and wavelength of the ridge–trough couplet are also closely related to the dynamical forcing for the SH, whereas our algorithm for detecting the LSTR and LSTT does not account for their amplitude and wavelength. In addition, a preconditioned surface cold anomaly over western Siberia is also very important for the intraseasonal amplification of the SH (Takaya and Nakamura 2005). Therefore, how the LSTR and LSTT, with other prerequisites, affect the SH deserves future investigation. We hope to address this issue in future work.
It has long been known that large-scale tilted (or transverse) ridge and trough systems are of essential importance to extreme climate and weather events (Section of Synoptic and Dynamic Meteorology, Institute of Geophysics and Meteorology, Academia Sinica 1958; Chang and Lau 1980; Uccellini et al. 1985; Bradbury et al. 2002; Peng and Bueh 2012; among others). However, the dynamics involved have not yet been understood in depth or systematically researched. One reason for this is possibly the lack of a statistical basis built on an objective identification method for large-scale tilted (or transverse) ridge and trough systems. Therefore, the identification method in the present study is expected to provide support for the further dynamical investigation of these large-scale systems.
We sincerely thank Prof. Tim D. Hewson and Dr. Ron McTaggart-Cowan, for giving us sound criticism and detailed comments that have led to the improvement of our paper. We also thank two anonymous reviewers for their valuable comments. We also convey our sincere thanks to Mr. Andrew Shearer for helping us to polish this paper. This work was jointly supported by the National Natural Science Foundation of China (Grant 41375064) and the National Key Technologies R&D Program of China (Grant 2015BAC03B03). The figures in this study are plotted using NCARG Command Language (UCAR/NCAR/CISL/VETS 2012).
To describe low-frequency components of Z500 fields, a Lanczos low-pass filter (Duchon 1979) with 121 weights defined as
where and n = 60. The cutoff frequency is 0.125 day−1 (8 days) and the sampling interval is 1 day. More details on the Lanczos filter are presented in Duchon (1979). Figure A1 shows the frequency response of this low-pass filter. With an 8-day cutoff period, the low- (high) frequency band has the frequency response approximately equal to 1 (0).